5-6 Newton’s Law of Universal Gravitation Therefore, the gravitational force must be proportional to both masses. By observing planetary orbits, Newton.

5-6 Newton’s Law of Universal Gravitation

Therefore, the gravitational force must be proportional to both masses.

By observing planetary orbits, Newton also concluded that the gravitational force must decrease as the inverse of the square of the distance between the masses.

In its final form, the Law of Universal Gravitation reads:

where

(5-4)

5-6 Newton’s Law of Universal Gravitation

The magnitude of the gravitational constant G can be measured in the

laboratory.

This is the Cavendish experiment.

5-7 Gravity Near the Earth’s Surface; Geophysical Applications

Now we can relate the gravitational constant to the local acceleration of gravity. We know that, on the surface of the Earth:

Solving for g gives:

Now, knowing g and the radius of the Earth, the mass of the Earth can be calculated:

(5-5)

5-7 Gravity Near the Earth’s Surface; Geophysical Applications

The acceleration due to gravity varies over the Earth’s surface due to altitude, local geology, and the shape of the Earth, which is not quite spherical.

5-8 Satellites and “Weightlessness”

Satellites are routinely put into orbit around the Earth. The tangential speed must be high enough so that the satellite does not return to Earth, but not so high that it escapes Earth’s gravity altogether.

5-8 Satellites and “Weightlessness”

The satellite is kept in orbit by its speed – it is continually falling, but the Earth curves from underneath it.

5-8 Satellites and “Weightlessness”

Objects in orbit are said to experience weightlessness. They do have a gravitational force acting on them, though!

The satellite and all its contents are in free fall, so there is no normal force. This is what leads to the experience of weightlessness.

5-8 Satellites and “Weightlessness”

More properly, this effect is called apparent weightlessness, because the gravitational force still exists. It can be experienced on Earth as well, but only briefly:

5-9 Kepler’s Laws and Newton's Synthesis

Kepler’s laws describe planetary motion.

1. The orbit of each planet is an ellipse, with the Sun at one focus.

5-9 Kepler’s Laws and Newton's Synthesis

2. An imaginary line drawn from each planet to the Sun sweeps out equal areas in equal times.

5-9 Kepler’s Laws and Newton's Synthesis

The ratio of the square of a planet’s orbital period is proportional to the cube of its mean distance from the Sun.

5-9 Kepler’s Laws and Newton's Synthesis

Kepler’s laws can be derived from Newton’s laws. Irregularities in planetary motion led to the discovery of Neptune, and irregularities in stellar motion have led to the discovery of many planets outside our Solar System.

5-10 Types of Forces in Nature

Modern physics now recognizes four fundamental forces:

1. Gravity

2. Electromagnetism

3. Weak nuclear force (responsible for some types of radioactive decay)

4. Strong nuclear force (binds protons and neutrons together in the nucleus)

5-10 Types of Forces in Nature

So, what about friction, the normal force, tension, and so on?

Except for gravity, the forces we experience every day are due to electromagnetic forces acting at the atomic level.

Summary of Chapter 5

• An object moving in a circle at constant speed is in uniform circular motion.

• It has a centripetal acceleration

• There is a centripetal force given by

•The centripetal force may be provided by friction, gravity, tension, the normal force, or others.

• Newton’s law of universal gravitation:

•Satellites are able to stay in Earth orbit because of their large tangential speed.

Summary of Chapter 5